Skip to main content
Log in

A Posteriori Error Estimates for Approximate Solutions of Linear Parabolic Problems

  • Numerical Methods
  • Published:
Differential Equations Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

REFERENCES

  1. Samarskii, A.A., Teoriya raznostnykh skhem (Theory of Difference Schemes), Moscow, 1989.

  2. Bakhvalov, N.S., Chislennye metody (Numerical Methods), Moscow, 1975.

  3. Thomee, V., Lecture Notes in Mathematics, Berlin, 1984, vol. 1054.

  4. Cockburn, B., Z. Angew. Math. Mech., 2003, vol. 83, no.11, pp. 731–754.

    Article  Google Scholar 

  5. Zienkiewicz, O.C. and Zhu, J.Z., Int. J. Numer. Meth. Engrg., 1987, vol. 24, pp. 337–357.

    Article  Google Scholar 

  6. Nochetto, R.H., Schmidt, A., and Verdi, C., Math. Comp., 1999, vol. 69, no.229, pp. 1–24.

    Article  Google Scholar 

  7. Repin, S., Math. Comput., 2000, vol. 69, no.230, pp. 481–500.

    Article  Google Scholar 

  8. Repin, S.I., Proceedings of the St. Petersburg Mathematical Society, 2002, vol. 9, pp. 143–171.

    Google Scholar 

  9. Neittaanmaki, P. and Repin, S., Reliable Methods for Mathematical Simulation. Error Control and a Posteriori Estimates, New York: Elsevier, 2004.

    Google Scholar 

  10. Repin, S., Rend. Mat. Lincei. Ser. 9, 2002, vol. 13, pp. 121–133.

    Google Scholar 

  11. Gaevskaya, A.V. and Repin, S.I., Mater. 5 vseros. sem. “Setochnye metody dlya kraevykh zadach i prilozheniya” (Proc. 5 Rus. Sem. “Grid Methods for Boundary Value Problems and Applications), Kazan, 2004, pp. 40–43.

  12. Ladyzhenskaya, O.A., Kraevye zadachi matematicheskoi fiziki (Boundary Value Problems of Mathematical Physics), Moscow, 1973.

  13. Ladyzhenskaya, O.A., Solonnikov, V.A., and Ural'tseva, N.N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa (Linear and Quasilinear Equations of Parabolic Type), Moscow, 1967.

  14. Aintworth, M. and Oden, J.T., A Posteriori Error Estimation in Finite Element Analysis, New York, 2000.

  15. Babuska, I. and Reinboldt, W.C., Int. J. Numer. Meth. Engrg., 1978, vol. 12, pp. 1597–1615.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Differentsial'nye Uravneniya, Vol. 41, No. 7, 2005, pp. 925–937.

Original Russian Text Copyright © 2005 by Gaevskaya, Repin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gaevskaya, A.V., Repin, S.I. A Posteriori Error Estimates for Approximate Solutions of Linear Parabolic Problems. Diff Equat 41, 970–983 (2005). https://doi.org/10.1007/s10625-005-0237-8

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10625-005-0237-8

Keywords

Navigation